## About

11

Publications

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Introduction

Dr. Richard Klitzing currently works at Their current project is 'Polytopes'.

Education

October 1985 - January 1996

## Publications

Publications (11)

The snub cube and the snub dodecahedron are well-known polyhedra since the days of Kepler. Since then, the term " snub " was applied to further cases, both in 3D and beyond, yielding an exceptional species of polytopes: those do not bow to Wythoff's kaleidoscopical construction like most other Archimedean polytopes, some appear in enantiomorphic pa...

The set of uniform polyhedra is grouped into classes of figures with the same edge skeletons. For each class one representative is chosen. Each such class is investigated further for other polyhedra with regular faces only, following the constraint that the edges remain a non-empty subset of the skeleton under consideration.

Polytopes with all vertices both (A) on a (hyper-) sphere and (B) on a pair of parallel (hyper-) planes, and further (C) with all edges of equal length I will call segmentotopes. Moreover, in dimensions 2, 3 and 4 names like segmentogon, segmentohedron, and segmentochoron could be used. In this article the convex segmentotopes up to dimension 4 are...

. The discrete part of the diffraction pattern of self-similar tilings, called the Bragg spectrum, is determined. Necessary and sufficient conditions for a wave vector q to be in the Bragg spectrum are derived. It is found that the Bragg spectrum can be non-trivial only if the scaling factor # of the tiling is a PV-number. In this case, the Bragg s...

The cell geometry of the six-dimensional bcc lattice is investigated. Via klotz construction two different classes of icosahedrally projected quasiperiodic tilings are defined. For both cases we determine the acceptance domains of tiles and give a detailed description of the geometry of all tiles.

1. Mustererzeugung durch Projektion / 2. Mustererzeugung durch Substitution / 3. Inflation und Deflation / 4. Hochhebung / 5. Weitere Definitionen / 6 Matching Rules / 7. Muster der Ebene mit fraktalen Hyperflächen / 8. Rekursion der Fourier-Transformationen / A. Anhang: Pisot-Vijayaraghavan-Zahlen
ISBN 978-3-86064-428-7

Two 1D sequences are discussed, which prove to have vanishing Bragg intensities with respect to k = 0, olthough their Limit translational modules are not empty. A 3D embedding is given as well, in order to understand this phenomenon from the cut-and-project Scenario. Both sequences can be interpreted as cross-sections of 2D 7-fold resp. 14-fold til...

Aperiodic crystalline structures, commonly called quasicrystals, display a great variety of combinatorially possible local configurations. The local configurations of first order are the vertex configurations. This paper investigates, catalogues and classifies in detail the latter in the following important two-dimensional cases: the Penrose tiling...

Simple quasiperiodic tilings with 8-fold and 12-fold symmetry are presented that possess local de-/inflation symmetry and perfect matching rules. The special feature of these tilings is that the full information is already derivable from the set of vertex sites alone. This means that the latter is a valid representative of the corresponding equival...

We generate a quasiperiodic, dodecagonally symmetric tiling of the plane by squares and equilateral triangles embedded in a higher-dimensional periodic structure. Starting from a 4D lattice frequently used for the embedding of dodecagonal structures, we iteratively construct an acceptance domain (AD) for a quasiperiodic point set which proves to be...

## Projects

Projects (2)

Research for and evaluation of higher dimensional polytopes. Extension of Dynkin symbol description. Evaluation of full incidence matrices.